Statistical methodology for binary data from a set of partially structured two-way random cross-classifications

A complete two-way cross-classification design is not practical in many settings. For example, in a toxicological study where 30 male rats are mated with 30 female rats and each mating outcome (successful or unsuccessful)is observed, time and resource considerations can make the use of the complete design prohibitively costly. Partially structured variations of this design are, therefore, of interest (e.g., the balanced disjoint rectangle design, the fully diagonal design, and the "S"-design). Methodology for analyzing binary data from such incomplete designs is illustrated with an example. This methodology, which is based on infinite population sampling arguments, allows the estimation of the mean response, among-row correlation coefficient, among-column correlation coefficient, and the within-cell correlation coefficient as well as their standard errors.     

Bivariate distributions of some ratios of independent noncentral chi-square random variables

The bivariate distributions of three pairs of ratios of in¬dependent noncentral chi-square random variables are considered. These ratios arise in the problem of computing the joint power function of simultaneous F-tests in balanced ANOVA and ANCOVA. The distributions obtained are generalizations to the noncentral case of existing results in the literature. Of particular note is the bivariate noncentral F distribution, which generalizes a special case of Krishnaiah*s (1964,1965) bivariate central F distribution. Explicit formulae for the cdf's of these distribu¬tions are given, along with computational procedures     

A note on Pitman's measure of closeness with balanced loss function

In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results.     

A note on Stein-type shrinkage estimator in partial linear models

In this paper, an exact sufficient condition for the dominance of the Stein-type shrinkage estimator over the usual unbiased estimator in a partial linear model is exhibited. Comparison result is then done under the balanced loss function. It is assumed that the vector of disturbances is typically distributed according to the law belonging to the sub-class of elliptically contoured models. It is also shown that the dominance condition is robust. Furthermore, a nonparametric estimation after estimation of the linear part is added for detecting the efficiency of the obtained results.     

(Un)expected exception: validating acquiescent response style factor in the Czech Republic

ABSTRACT

This study explores the acquiescent response style (ARS) among respondents in the Czech Republic. To analyse ARS, confirmatory factor analysis (CFA) was employed and the response style (RS) was modelled as a latent variable. The RS factor in the CFA model must be validated by its relationship to education and age, i.e. proxies of cognitive ability. The two studies presented in this article use large amount of data as all available balanced batteries of items were analysed. In Study 1, the RS factor showed no correlation with age/education in most of the models. Study 2 employed additional measures of cognitive ability and education and confirmed the overall absence of the relationship. Author concludes that the modelled RS factor then cannot be considered the ARS and deduces that the most likely explanation of the identified systematic error variance is the respondents’ carelessness manifested by automatically choosing the extreme agreement, or choosing the first presented answer as a result of memory effect.     

The Parshvanath yantram yields a constant-sum partially balanced incomplete block design

Yantrams have been used to generate mixture designs in the interior of a simplex. In this note, we show a connection between Parshvanath yantram and a particular partially balanced incomplete block design. This block design is rather special and somewhat unexpected due to the feature that sum of the treatment symbols in any block is constant.     

Games Played Through Agents

We introduce a game of complete information with multiple principals and multiple common agents. Each agent makes a decision that can affect the payoffs of all principals. Each principal offers monetary transfers to each agent conditional on the action taken by the agent. We characterize pure‐strategy equilibria and we provide conditions—in terms of game balancedness—for the existence of an equilibrium with an efficient outcome. Games played through agents display a type of strategic inefficiency that is absent when either there is a unique principal or there is a unique agent.     

Remove unwanted variation retrieves unknown experimental designs

Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV-inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV-inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV-inverse recovers intra- and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE.     

推进城乡义务教育均衡发展的财政政策分析

教育的发展是关乎国家发展的大事,尤其是义务教育阶段的发展,直接关系着我国人才培养的质量和水平。近年来,由于教育政策的倾斜,出现了义务教育阶段的区域、城乡、校际以及教育群体之间的不均衡。文章从国家财政政策的角度对义务教育均衡发展问题进行分析,揭示了当前我国义务教育发展不均衡的基本状况,剖析了其根本原因所在,并从加大政府教育财政投入、合理分配各地区教育经费、建议实施区域内城乡生均均等化拨款制度和正确引导国民教育意识四个方面提出对策建议。